Reading and Interpreting Graphs Let C be the function whose graph is given in the next column. This graph represents the cost C of manufacturing q computers in a day.

(a) Determine C(0). Interpret this value.

(b) Determine C(10). Interpret this value.

(c) Determine C(50). Interpret this value.

(d) What is the domain of C? What does this domain imply in terms of daily production?

(e) Describe the shape of the graph.

(f) The point (30, 32000) is called an inflection point. Describe the behavior of the graph around the inflection point.

We have given graph is,

Let C be the function whose graph is given below. This graph represents the cost C of manufacturing q computers in a day.

Here we can use co-ordinates $(x,y)$.

Here y represent the corresponding value of function at x.

The point of inflection or inflectionpoint is a point in which the concavity of the function changes.

Domain of the function is the set of all input values where the function is defined and real.

In the given graph the points on the vertical axis is of the $(q,C(q\left)\right)$ form.

From the graph we have initial cost is 5000.

That is $C\left(0\right)=5000$.

Hence, value for C(0) is 5000.

From the given graph cost for manufacturing 10 computers is 19000.

That is, $C\left(10\right)=19000.$

Hence, value for $C\left(10\right)$ is 19000.

From the graph cost of manufacturing 50 computers in a day is 51,000.

That is $C\left(50\right)=51,000$.

Hence value for $C\left(50\right)$ is 51,000.

Here domain of the function is the set of values of q.

So domain of the function is $[0,100]$

Domain represent the manufacturing q computers in a day.

Hence, domain of the function is $[0,100]$

Domain represent the manufacturing q computers in a day.

The given graph has single inflection point and we know that the graph of a cubic function always has single inflection point.

So the shape of given graph is cubic.

The graph is increasing slowly up to

q = 30 and start to increase more rapidly around q = 50.

Shape for the given graph is cubic.

We have (30, 32,000) is the inflection point.

Inflection point represent the cost of computers increasing grows from growing slow to growing rapidly.

Inflection point represent the cost of computers increasing grows from growing slow to growing rapidly.